Officially 4.3 is the last firmware for a GT-I9300, however there are custom 4.4.x (x = 4, 3 or 2) ROMs for it. Choose one carefully and follow all the instructions to the letter for installing it. Any confusion in the instructions and come back here with the link to the chosen ROM and your questions and I'll be happy to help.

 

Yes, installing custom firmwares does void your warranty. Flashing ROMs, modifications, rooting (think admin rights to everything) etc. your phone can also can destroy your phone (software) making it a shiny lump of electronics, ie a "brick", but you would have to something completely stupid, rather than make a mistake, to do so.

If your new to smartphones, and Android in particular, get to know your device, play with it, etc and most importantly, and I'm not being flippant or sarcastic here, read here and use Google. If I were you I'd use your phone and not try updating or modifying it yet, the Galaxy SIII is, even today a fine and decent smartphone.

We all were completely new to smartphones and Android once, if you have any question, no matter how silly you think it is - ask.